In the statement from the White House, the former senator is referred to as "Scott Brown of MA".
This would be a major boost for Brown's political career, which faltered after his 2012 loss to Warren was followed by a defeat in the 2014 New Hampshire Senate race to Democratic candidate Jeanne Shaheen.
It was reported a couple of months ago that Brown was under consideration for the ambassadorship after Shulkin was named the VA chief. Brown was supporting Trump's presidential bid at that time. Scott Brown for ambassador to New Zealand. "I'm confident he will devote his unmatched work ethic and experience to this new opportunity and I wish Scott and Gail the best of luck on this new endeavor".
Brown is a lawyer and former state legislator who served in the Massachusetts Army National Guard. New Zealand for decades has collaborated with the U.S. as part of the so-called Five Eyes alliance, which also includes Canada, Great Britain, and Australia.
He then moved to New Hampshire, ran for Senate there, and lost again.
Since leaving the Senate, Mr Brown has stayed in the public eye as a political pundit on the Fox News Channel, and was an early backer of Mr Trump's campaign for the presidency.
Trump aides did not immediately respond to requests for additional information.